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Yesterday, a question entitled Is Euclid dead? has been asked in which the OP states:

"Currently I am leading a campaign for the return of EG to the syllabus of the high schools of my country (Cyprus) and I would like to hear arguments FOR the return of EG in high schools."

Within about a day, this question received more than 7000 views, which seems hardly possible without more-or-less massively advertising it outside MO, and its score raised to about 50. It was closed, quickly reopened and now closed again. It received 10 answers so far.

Given that this question was all-in-all received so extraordinarily well: is it really considered good practice to ask a question on MO to promote some campaign and gather arguments in favor of it?

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    $\begingroup$ Stefan, would your opinion of the suitability of this question be changed if the quoted text were replaced by "I am interested in hearing arguments for and against the teaching of EG in high schools"? $\endgroup$ – Todd Trimble Dec 21 '13 at 0:25
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    $\begingroup$ @Todd: I think it would be a little better, but I'd say the close reason "primarily opinion-based" would still apply perfectly. $\endgroup$ – Stefan Kohl Dec 21 '13 at 0:29
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    $\begingroup$ Judging from the answers given, I honestly would be hard pressed to argue with that close reason. $\endgroup$ – Todd Trimble Dec 21 '13 at 0:32
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    $\begingroup$ In 'defence' of the quetsion "Also, any arguments AGAINST EG would be welcome." is (and always was) the last sentence of the question. $\endgroup$ – user9072 Dec 21 '13 at 0:44
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    $\begingroup$ Is there a way to check what quid said in comments on the initial question, and then Stephan here, that an unusual proportion of the view and up votes for this question comes from users who don't usually participate to mathoverflow but I suppose, got the reputations needed to vote by linking their account here to anoth account on stack exchange? If so, I would be very interested to know it. $\endgroup$ – Joël Dec 21 '13 at 4:20
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    $\begingroup$ @Joël Exactly. The question has so many views and upvotes, because it was promoted in the hot list to the whole Stack Exchange network, therefore the many votes (due to the association bonus) and views do not necessarily mean that the MO community itself likes the question that much indeed. Maybe MathOverflow should consider to ask Stack Exchange to exclude questions from this site from the hot list, to prevent "external" votes and views from distorting the take of the MO community on certain questions too much, if such effects are not wanted? $\endgroup$ – Dilaton Dec 21 '13 at 9:30
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    $\begingroup$ @Joël: There is at least one deleted answer by a 101 points user with various accounts on the network but not on MO and not in a relevant way on math.SE either. (BTW there are at least three deleted answers, just as aside to judge the general quality.) For the views is is based on observation MO questions even very popular ones just never got that many views so quickly. However, I am sure many regular users also appreciate the question. I am against it, but to claim it is only 'outsiders' would be too simple. What is however also noteworty is the large number of downvotes. $\endgroup$ – user9072 Dec 21 '13 at 11:07
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    $\begingroup$ I offer this as one more bit of evidence against the association bonus. See meta.mathoverflow.net/questions/435/the-association-bonus $\endgroup$ – Steven Landsburg Dec 21 '13 at 13:47
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    $\begingroup$ The hot questions list amplifies votes, but the question has to be popular with the native users to get on the list in the first place. I also suspect that there are external links that drive traffic, the hot questions list typically results in only around 1000 views, unless the question is in the list for several days. $\endgroup$ – Mad Scientist Dec 21 '13 at 14:52
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    $\begingroup$ Mad Scientist, how does a question gets on the "hot question list"? $\endgroup$ – Joël Dec 21 '13 at 15:32
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    $\begingroup$ Not certain this is still current but the formula for 'hotness' of q question can be seen meta.stackexchange.com/questions/11602/… and I think it is basically sorted by this likely with some tweaking. The main problem with this formula is that it gives way too much emphasis to having many answers ( directly and via answer score). $\endgroup$ – user9072 Dec 21 '13 at 17:16
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    $\begingroup$ @MadScientist In my experience with the new hot questions list, the incoming traffic can easily be at the levels suggested given the circumstances. This question was at the top of the list for the better part of a day, which means it was in the top 3 and was displayed even on post pages. I've tracked a couple of questions that made it to that level, and as soon as they did they started bringing in hits at around 1k every hour or so. On the old drop-down it was rare for a question to get over a few thousand views that way, but the new one seems much more influential at least for the top 3. $\endgroup$ – Logan M Dec 22 '13 at 9:49
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    $\begingroup$ As a note, for the Math SE perspective on the hot questions list, see meta.math.stackexchange.com/questions/12161 and meta.math.stackexchange.com/q/11994. I think there's a lot of good evidence there that this is not something that MO should be involved in if we can avoid it. $\endgroup$ – Logan M Dec 23 '13 at 7:16
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    $\begingroup$ @StefanKohl this question would need 6 votes (the absolute max would be 10 and min 3, IIRC). On the other point: it is standing policy agreed upon via various discussions on the old meta that such questions are not deleted. If/when a couple of users deviate from this policy by still voting to delete a moderator could and should step in to correct this deviation from existing policy. If somebody wants to change the existing policy they are of course welcome to start another (general) discussion. (cont.) $\endgroup$ – user9072 Dec 28 '13 at 17:47
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    $\begingroup$ Moreover, at least on old MO [but I think this still is the case except for the global daily max of delte votes], it was unreasonable to have 'the community' decide via voting over deletion as in contrast to other votes one could vote for un/deletion of the same question again, so that 3 users on each side could have un/delete the same question 'infinitely' many times. $\endgroup$ – user9072 Dec 28 '13 at 17:53
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(I started to write this right after the meta-question got asked, but due to deletion can only finish it now.)

I cast the final vote for the second closure. My reason was not so much that this is part of some 'campaign' (likely this is a language issue, and OP could just have used another formulation). But rather that it is not even clear what this is about precisely.

Teaching Euclidean geometry is not a precise notion, and OP did not do enough (IMO) to make precise what they have in mind and what is feasible. Also, various answers assume, directly or indirectly, a certain way of teaching it.

To say something positive, too. I think some of the answers and other contributions, which in part contain interesting and thoughtful remarks, in fact mainly showed that the original question was not precise and focused enough.

Thus, I propose we leave this question closed (edited or not). Everybody who wishes to continue Q&A in this direction could inform themselves about things to keep in mind when asking based on this question.

I think that if the goal is to continue with some scientific or at least focused and calm exchange on the subject it will be better to take it to less visible and more focused questions, as oposed to continuing on this highly visible one that already contains too much tangential and provocative contributions.

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    $\begingroup$ Yes, the lack of precision makes answering the question well-nigh possible. Should EG be taught in secondary schools? Why or why not? is not a reasonable research question. If the goal is to gain personal opinions from mathematicians (their "two cents") then the query is fine. If the goal is to gain substantive evidence for or against the teaching of EG, then many more specifics need to be put in. Consider questions like Should every undergraduate take topology? Why or why not? or Should Calculus be learned in Physics classes? Why or why not? (cont'd) $\endgroup$ – Benjamin Dickman Dec 22 '13 at 2:39
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    $\begingroup$ To me, these questions are also ill-posed, and I somehow imagine they would've been closed down much more quickly. I'm not quite sure why the EG question has so many up-votes; I can say that I used one of my three down-votes for it, and that I think it gives a warped view of what an appropriate Mathematics Education question looks like. (cont'd) $\endgroup$ – Benjamin Dickman Dec 22 '13 at 2:40
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    $\begingroup$ I left one book recommendation there; perhaps Sinclaire's The History of the Geometry Curriculum in the United States is a better one - note that it includes a chapter entitled The Bourbaki Group and its Impact on Geometry. But I don't have this book handy, I have never read it, and I don't even understand the question well enough to know if this is useful information. Would it be better to delve into a specific area of EG impact? (cont'd once more) $\endgroup$ – Benjamin Dickman Dec 22 '13 at 2:40
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    $\begingroup$ E.g., Usiskin's The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry (jstor.org/stable/748492)? I am game for bringing a Math-Ed perspective to Math-Ed questions, but only if they are held to the same high standards (or higher ones!) applied to questions in pure mathematics. [Sorry to leave so many comments; I just don't think my answer qualifies as a response to the actual meta-question posed here.] $\endgroup$ – Benjamin Dickman Dec 22 '13 at 2:41
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    $\begingroup$ Thanks for the detailed elaboration, @BenjaminDickman. I will take the oppurtunity to quote OP of question latest comment "EG is not taught in American high-schools. At least not the kind I am campaining for! – smyrlis 4 hours ago" leaving open the detail what exactly even is campaigned for, and confirming further that it is a bit unclear what is to be discussed. $\endgroup$ – user9072 Dec 22 '13 at 3:02
  • $\begingroup$ I do not think that "Euclidean geometry" is ambiguous when we're talking about its return to high school. In this case, it is about proofs for Pythaogras, Thales, and the basic theorems on triangles and circles. And given the sorry state of mathematical education at schools the whole wide world over I would have thought this is a legitimate question . . . $\endgroup$ – Franz Lemmermeyer Dec 25 '13 at 17:31
  • $\begingroup$ @FranzLemmermeyer it is visible on main and meta that there was some confusion (not directly involving me) what is meant precisely. When the comment of OP I quoted was made this confusion was clearly visible. To then only say this, as opposed to say at least something at the level of detail you say is in my opinion a strange thing to do. If they run a campaign, I'd assume they have a clear idea, why not share it? Also, do you maintain there is exactly one way to have a curriculum for EG (also at the level of detail relevant for the question)? $\endgroup$ – user9072 Dec 26 '13 at 0:07
  • $\begingroup$ (cont.) Your last sentence is very strange for me. Likely it is a legitimate question. Though personally I do find somebody asking for arguments to support the idea of a camapaign they already started a bit odd. To ask first and then decide about the campaign would seem like a more natural way to proceed to me. Yet, the perceived state of schools should not be that relevant to decide whether the q is legitimate. And, just that it is a legitimate question does not make it suitable for this site. $\endgroup$ – user9072 Dec 26 '13 at 0:16
  • $\begingroup$ (cont.) But as said I have no problem with q on geometry education in schools getting asked here. It is just that this particular one was not good in various ways. In addition I really do not think that some (research) mathematcicians without any particular expertise in high-school teaching voicing their opinions is the best way to approach this; and this is mainly what happened. As I said on a I think deleted answer it seemed the main source of information in some cases was one's own courses or those of ones kids. (To be clear, mainly this includes me, but also I did not given an answer.) $\endgroup$ – user9072 Dec 26 '13 at 0:24
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The question if and how should Euclidean geometry be taught in high-schools is among the most crucial and interesting possible questions in the category "mathematical education." So overall I welcome such an (appropriately written/edited) question to MO.

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    $\begingroup$ Why do you think so? -- Euclidean geometry is only one of various topics in mathematics taught in high schools, and I think it is certainly not the most important one. -- What about, e.g., introducing basic algebraic structures (groups, rings, fields), or really proving the things taught in calculus? $\endgroup$ – Stefan Kohl Dec 21 '13 at 17:11
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    $\begingroup$ Dear Stefan: Euclidean geometry (with proofs) was an important part of mathematical education in the ninth grade (14 yo) when I was a high school student. (And in many other places) What I said was that the place of EG in high school education is an important question. I welcome this question to MO, although naturally for math education questions we cannot expect the same level of precision and objectivity as for others. $\endgroup$ – Gil Kalai Dec 21 '13 at 17:16
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    $\begingroup$ Not the same does not mean none at all. Actual professionals in math education expressed concerns about the question. $\endgroup$ – user9072 Dec 21 '13 at 17:18
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    $\begingroup$ Regarding my own opinion on your suggestions: I don't support teaching what you suggest to teach "introducing basic algebraic structures (groups, rings, fields), or really proving the things taught in calculus?" in high school (certainly not in 9th and 10th grades which were the two years EG was often taught). I like the idea that EG will be taught but did not study this issue. $\endgroup$ – Gil Kalai Dec 21 '13 at 17:19
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    $\begingroup$ Quid, "Actual professionals in math education expressed concerns about the question". What do you refer to? the MO question? or the question of teaching EG in high school? $\endgroup$ – Gil Kalai Dec 21 '13 at 17:21
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    $\begingroup$ Sorry for the rushed comment. The MO question. More specifically the comment of Benjamin Dickman. Also it seems to me Amir Asghari does not fully endorse the question, though to say he expressed concerns might be too strong. In addition, as pointed out (though not critically) there is a lot of literature. Is OP aware fo it? If not is this research level? Sorry got to go. $\endgroup$ – user9072 Dec 21 '13 at 17:45
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    $\begingroup$ ahh, I got it. I did not follow the earlier versions, and discussion. My answer here is mainly about evaluating the question: "Should Euclidean geometry be taught in high-schools?" $\endgroup$ – Gil Kalai Dec 21 '13 at 18:30
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    $\begingroup$ So you voted to reopen without first making yourself familiar with the situation?! $\endgroup$ – user9072 Dec 21 '13 at 20:03
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    $\begingroup$ yes indeed, it was based on the revised question. $\endgroup$ – Gil Kalai Dec 21 '13 at 20:14
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    $\begingroup$ Mathematics Education has many questions of great interest. How should one teach division of fractions? or (in the U.S.) How should instructors who have never formally learned about Mathematical Modeling teach it now that it's a part of the Common Core State Standards? But these two questions, along with the one about EG in secondary schools, are big umbrella questions. (cont'd) $\endgroup$ – Benjamin Dickman Dec 22 '13 at 3:04
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    $\begingroup$ They are good to have in one's mind, but they need to be sharpened to a far greater extent if there is to be any hope of answering them meaningfully. Some who respond will do the sharpening themselves; I think, in this context, such an expectation is unreasonable on MO. Others will simply state their opinions, and while it is nice to know how some prominent mathematicians feel about questions in Mathematics Education, it can also do the discipline of Math Ed an injustice by not treating it as an area of rigorous research. $\endgroup$ – Benjamin Dickman Dec 22 '13 at 3:05
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    $\begingroup$ Thanks Benjamin. I agree with you. I just thought that the edited question is reasonable, the editing effort deserves a praise, and the question itself deserves a new try. I agree that questions in math Ed should be sharp, and hopefully attract also math Ed experts. It goes without saying that math education requires understanding that professional mathematicians dont have automatically. The relations between professional math teachers, professonal math education people, and professional mathematicians are rather complex. $\endgroup$ – Gil Kalai Dec 22 '13 at 19:05
  • $\begingroup$ @Stefan: in which country is Euclidean geometry currently taught at school? $\endgroup$ – Franz Lemmermeyer Dec 25 '13 at 17:33
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The campaign doesn’t bother me one way or the other, especially since the author was clear they were interested in arguments from both sides. But subjective, discussion-y, primarily opinion-based are things that MO (like most SE sites) has chosen to reject since the very early days — they may be interesting, on-topic, and generate good answers, but they don’t fit the SE format well, and (the general consensus has mostly been) they aren’t a good influence on the long-term quality of the site.

So, in sum: If a question is otherwise a good question, and just happens to be related to a campaign, I don’t see any reason to reject it. This question was (though very interesting) unsuitable for MO for other reasons, hence I support its closure.

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"No", would be an obvious answer to the "or" part of your question. But, to be honest, your question explicitly includs a strong judgment that is even more opinion based than original question! To be explicit, I am not sure that there is (was) some explicit mis-intention behind the question.

But about the MO question, I am quite in agreement with you, quid (or Quid :-) ) and Todd that the original question is primarily opinion-based and I also believe even by making the terms used as precise as possible (see quid's or Gil's answer) the question remains opinion based, since such decisions (what to teach, how to teach) are basically value-laden.

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  • $\begingroup$ "such decisions (what to teach, how to teach) are basically value-laden" Is this statement so obvious that it needs no explanation? At least some such decisions are not value-laden. $\endgroup$ – Did Dec 26 '13 at 10:06
  • $\begingroup$ @Did Decide! Should we teach long division or not? If yes, how, if no, why? Just do it as a thought experiment! $\endgroup$ – Amir Asghari Dec 26 '13 at 10:51
  • $\begingroup$ Sorry but I am feeling something like an excess of testosterone here... Anyway, you might want to explain which values long division is value-laden with. $\endgroup$ – Did Dec 26 '13 at 17:36
  • $\begingroup$ @Did Sorry if I haven't tried to be more clear. Let me tell you a story. Once upon a time I was teacher. There was a very strange algorithm for finding square root of a number in the text book that I should teach. If you had more advanced concepts you could find some meaning behind that algorithm. But my students were just in middle school, and without those concepts, the algorithm remained just a meaningless set of rules. I decided not to go with the textbook's suggestion. Instead, I went a more conceptual approach (to be continued) $\endgroup$ – Amir Asghari Dec 26 '13 at 22:59
  • $\begingroup$ @Did according to which, my students could approximate the square root of a number by trial and error by rescaling an square without learning that algorithm. So far so good. Next meeting with parents, they came to me asking me why I didn't teach that algorithm. One of them said, my boy is going to be an engineer and without knowing how to find the square root of a number how he could become an engineer! I answered, at that time he know how to use a calculator. All my argument didn't convince them. And later on, I forced to teach that algorithm. $\endgroup$ – Amir Asghari Dec 26 '13 at 23:10
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    $\begingroup$ @Did See, there was nothing wrong with that algorithm (and long division) in itself. The point is what you want from it, and when you want it. Here is where the values come into play. $\endgroup$ – Amir Asghari Dec 26 '13 at 23:12
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    $\begingroup$ @Did the first thing to decide is what is the purpose of teaching (math). This is pretty purely value-based. And a lot of subsequent discussions about 'details' depend on it. A certain tension (or perceived tension) around such things was implict in certain discussion on main on this question. $\endgroup$ – user9072 Dec 28 '13 at 13:47
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It appeared in the hot questions list and had an interesting title: as such, the number of views is unsurprising.

It was an interesting question that a non-mathematician can understand. As such, the number of favourites/votes is unsurprising. (I use favourites to track questions which seem interesting, or, on some sites, questions I think I should edit. I tend not to vote on sites where I don't know the subject, but I do mark favourites.)

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